论文标题
某些过度确定的自由边界问题的存在和对称结果
Existence and Symmetry results for some overdetermined free boundary problems
论文作者
论文摘要
在本文中，我们证明了一个验证某些积分不平等的域（严格地）包含在某些自由边界问题中，或者它与$ n $ - ball的相吻合。我们还提出了新的过度确定的价值问题，这些问题具有$ n $ - ball作为解决方案。为了达到我们的结果，我们使用涉及Dirichlet问题解决方案的域衍生物的整体身份。
In this paper, we prove that a domain which verifies some integral inequality is either (strictly) contained in the solution of some free boundary problem, or it coincides with an $N$-ball. We also present new overdetermined value problems which have an $N$-ball as a solution. To reach our results, we use an integral identity which involves the domain derivative of the solution of Dirichlet problem.
